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Invariance principles and Gaussian approximation for strictly stationary processes

Author(s): Dalibor Volný
Journal: Trans. Amer. Math. Soc. 351 (1999), 3351-3371.
MSC (1991): Primary 28D05, 60G10, 60F17, 60F05, 28D20
Posted: April 8, 1999
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Abstract: We show that in any aperiodic and ergodic dynamical system there exists a square integrable process $(f\circ T^{i})$ the partial sums of which can be closely approximated by the partial sums of Gaussian i.i.d. random variables. For $(f\circ T^{i})$ both weak and strong invariance principles hold.

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Additional Information:

Dalibor Volný
Affiliation: Université de Rouen, UPRES-A CNRS 60 85, Site Colbert, 76821 Mont-Saint-Aignan Cedex, France
Email: dalibor.volny@univ-rouen.fr

DOI: 10.1090/S0002-9947-99-02401-0
PII: S 0002-9947(99)02401-0
Keywords: Zero entropy stationary process, weak invariance principle, strong invariance principle, approximation by Gaussian random variables
Received by editor(s): February 21, 1997
Posted: April 8, 1999
Additional Notes: This research has been partially supported by the Grant Agency of the Charles University (Prague), grant #GAUK 6191
Copyright of article: Copyright 1999, American Mathematical Society

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